Zero-One Permanent is #P-Complete, A Simpler Proof
نویسندگان
چکیده
In 1979, Valiant proved that computing the permanent of a 01-matrix is #PComplete. In this paper we present another proof for the same result. Our proof uses \black box" methodology, which facilitates its presentation. We also prove that deciding whether the permanent is divisible by a small prime is #P-Hard. We conclude by proving that a polynomially bounded function can not be #P-Complete under \reasonable" complexity assumptions. 1
منابع مشابه
New Hardness Results for the Permanent Using Linear Optics
In 2011, Aaronson gave a striking proof, based on quantum linear optics, showing that the problem of computing the permanent of a matrix is #P-hard. Aaronson’s proof led naturally to hardness of approximation results for the permanent, and it was arguably simpler than Valiant’s seminal proof of the same fact in 1979. Nevertheless, it did not prove that computing the permanent was #P-hard for an...
متن کاملA Linear-Optical Proof that the Permanent is #P-Hard
One of the crown jewels of complexity theory is Valiant’s 1979 theorem that computing the permanent of an n × n matrix is #P-hard. Here we show that, by using the model of linearoptical quantum computing—and in particular, a universality theorem due to Knill, Laflamme, and Milburn—one can give a different and arguably more intuitive proof of this theorem.
متن کاملComparing Entropies in Statistical Zero Knowledge with Applications to the Structure of SZK
We consider the following (promise) problem, denoted ED (for Entropy Difference): The input is a pair of circuits, and YES instances (resp., NO instances) are such pairs in which the first (resp., second) circuit generates a distribution with noticeably higher entropy. On one hand we show that any language having a (honest-verifier) statistical zero-knowledge proof is Karpreducible to ED. On th...
متن کاملOne Terminal Digital Algorithm for Adaptive Single Pole Auto-Reclosing Based on Zero Sequence Voltage
This paper presents an algorithm for adaptive determination of the dead timeduring transient arcing faults and blocking automatic reclosing during permanent faults onoverhead transmission lines. The discrimination between transient and permanent faults ismade by the zero sequence voltage measured at the relay point. If the fault is recognised asan arcing one, then the third harmonic of the zero...
متن کاملThe factorization of the permanent of a matrix with minimal rank in prime characteristic
It is known that any square matrix A of size n over a field of prime characteristic p that has rank less than n/(p− 1) has a permanent that is zero. We give a new proof involving the invariant Xp. There are always matrices of any larger rank with non-zero permanents. It is shown that when the rank of A is exactly n/(p − 1), its permanent may be factorized into two functions involving Xp. Let n ...
متن کامل